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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Moduleslr.wasp
Title produced by softwareSimple Regression
Date of computationFri, 23 Oct 2009 00:28:29 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Oct/23/t1256279362hv0rso9wj6sy08p.htm/, Retrieved Thu, 02 May 2024 03:23:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=49838, Retrieved Thu, 02 May 2024 03:23:27 +0000
QR Codes:

Original text written by user:Simple regression
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact143

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
- RMPD  [Bivariate Explorative Data Analysis] [Shw4: Part 1. Are...] [2009-10-22 19:35:20] [3c8b83428ce260cd44df892bb7619588]
- RMP       [Simple Regression] [shw4: Simple regr...] [2009-10-23 06:28:29] [7a39e26d7a09dd77604df90cb29f8d39] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
87.28
87.28
87.09
86.92
87.59
90.72
90.69
90.3
89.55
88.94
88.41
87.82
87.07
86.82
86.4
86.02
85.66
85.32
85
84.67
83.94
82.83
81.95
81.19
80.48
78.86
69.47
68.77
70.06
73.95
75.8
77.79
81.57
83.07
84.34
85.1
85.25
84.26
83.63
86.44
85.3
84.1
83.36
82.48
81.58
80.47
79.34
82.13
81.69
80.7
79.88
79.16
78.38
77.42
76.47
75.46
74.48
78.27
80.7
79.91
78.75
77.78
81.14
81.08
80.03
78.91
78.01
76.9
75.97
81.93
80.27
78.67
77.42
76.16
74.7
76.39
76.04
74.65
73.29
71.79
74.39
74.91
74.54
73.08
72.75
71.32
70.38
70.35
70.01
69.36
67.77
69.26
69.8
68.38
67.62
68.39
66.95
65.21
66.64
63.45
60.66
62.34
60.32
58.64
60.46
58.59
61.87
61.85
67.44
77.06
91.74
93.15
94.15
93.11
91.51
89.96
88.16
86.98
88.03
86.24
84.65
83.23
81.7
80.25
78.8
77.51
76.2
75.04
74
75.49
77.14
76.15
76.27
78.19
76.49
77.31
76.65
74.99
73.51
72.07
70.59
71.96
76.29
74.86
74.93
71.9
71.01
77.47
75.78
76.6
76.07
74.57
73.02
72.65
73.16
71.53
69.78
67.98
69.96
72.16
70.47
68.86
67.37
65.87
72.16
71.34
69.93
68.44
67.16
66.01
67.25
70.91
69.75
68.59
67.48
66.31
64.81
66.58
65.97
64.7
64.7
60.94
59.08
58.42
57.77
57.11
53.31
49.96
49.4
48.84
48.3
47.74
47.24
46.76
46.29
48.9
49.23
48.53
48.03
54.34
53.79
53.24
52.96
52.17
51.7
58.55
78.2
77.03
76.19
77.15
75.87
95.47
109.67
112.28
112.01
107.93
105.96
105.06
102.98
102.2
105.23
101.85
99.89
96.23
94.76
91.51
91.63
91.54
85.23
87.83
87.38
84.44
85.19
84.03
86.73
102.52
104.45
106.98
107.02
99.26
94.45
113.44
157.33
147.38
171.89
171.95
132.71
126.02
121.18
115.45
110.48
117.85
117.63
124.65
109.59
111.27
99.78
98.21
99.2
97.97
89.55
87.91
93.34
94.42
93.2
90.29
91.46
89.98
88.35
88.41
82.44
79.89
75.69
75.66
84.5
96.73
87.48
82.39
83.48
79.31
78.16
72.77
72.45
68.46
67.62
68.76
70.07
68.55
65.3
58.96
59.17
62.37
66.28
55.62
55.23
55.85
56.75
50.89
53.88
52.95
55.08
53.61
58.78
61.85
55.91
53.32
46.41
44.57
50
50
53.36
46.23
50.45
49.07
45.85
48.45
49.96
46.53
50.51
47.58
48.05
46.84
47.67
49.16
55.54
55.82
58.22
56.19
57.77
63.19
54.76
55.74
62.54
61.39
69.6
79.23
80
93.68
107.63
100.18
97.3
90.45
80.64
80.58
75.82
85.59
89.35
89.42
104.73
95.32
89.27
90.44
86.97
79.98
81.22
87.35
83.64
82.22
94.4
102.18
Dataseries Y:
Download CSV
Histogram 
255
280.2
299.9
339.2
374.2
393.5
389.2
381.7
375.2
369
357.4
352.1
346.5
342.9
340.3
328.3
322.9
314.3
308.9
294
285.6
281.2
280.3
278.8
274.5
270.4
263.4
259.9
258
262.7
284.7
311.3
322.1
327
331.3
333.3
321.4
327
320
314.7
316.7
314.4
321.3
318.2
307.2
301.3
287.5
277.7
274.4
258.8
253.3
251
248.4
249.5
246.1
244.5
243.6
244
240.8
249.8
248
259.4
260.5
260.8
261.3
259.5
256.6
257.9
256.5
254.2
253.3
253.8
255.5
257.1
257.3
253.2
252.8
252
250.7
252.2
250
251
253.4
251.2
255.6
261.1
258.9
259.9
261.2
264.7
267.1
266.4
267.7
268.6
267.5
268.5
268.5
270.5
270.9
270.1
269.3
269.8
270.1
264.9
263.7
264.8
263.7
255.9
276.2
360.1
380.5
373.7
369.8
366.6
359.3
345.8
326.2
324.5
328.1
327.5
324.4
316.5
310.9
301.5
291.7
290.4
287.4
277.7
281.6
288
276
272.9
283
283.3
276.8
284.5
282.7
281.2
287.4
283.1
284
285.5
289.2
292.5
296.4
305.2
303.9
311.5
316.3
316.7
322.5
317.1
309.8
303.8
290.3
293.7
291.7
296.5
289.1
288.5
293.8
297.7
305.4
302.7
302.5
303
294.5
294.1
294.5
297.1
289.4
292.4
287.9
286.6
280.5
272.4
269.2
270.6
267.3
262.5
266.8
268.8
263.1
261.2
266
262.5
265.2
261.3
253.7
249.2
239.1
236.4
235.2
245.2
246.2
247.7
251.4
253.3
254.8
250
249.3
241.5
243.3
248
253
252.9
251.5
251.6
253.5
259.8
334.1
448
445.8
445
448.2
438.2
439.8
423.4
410.8
408.4
406.7
405.9
402.7
405.1
399.6
386.5
381.4
375.2
357.7
359
355
352.7
344.4
343.8
338
339
333.3
334.4
328.3
330.7
330
331.6
351.2
389.4
410.9
442.8
462.8
466.9
461.7
439.2
430.3
416.1
402.5
397.3
403.3
395.9
387.8
378.6
377.1
370.4
362
350.3
348.2
344.6
343.5
342.8
347.6
346.6
349.5
342.1
342
342.8
339.3
348.2
333.7
334.7
354
367.7
363.3
358.4
353.1
343.1
344.6
344.4
333.9
331.7
324.3
321.2
322.4
321.7
320.5
312.8
309.7
315.6
309.7
304.6
302.5
301.5
298.8
291.3
293.6
294.6
285.9
297.6
301.1
293.8
297.7
292.9
292.1
287.2
288.2
283.8
299.9
292.4
293.3
300.8
293.7
293.1
294.4
292.1
291.9
282.5
277.9
287.5
289.2
285.6
293.2
290.8
283.1
275
287.8
287.8
287.4
284
277.8
277.6
304.9
294
300.9
324
332.9
341.6
333.4
348.2
344.7
344.7
329.3
323.5
323.2
317.4
330.1
329.2
334.9
315.8
315.4
319.6
317.3
313.8
315.8
311.3

Tables (Output of Computation)





Simple Linear Regression - Ungrouped Data
ParameterValueS.E.T-STATNotes
Constant165.550098
Beta1.8416830.09701018.984375 H0: beta = 0
Elasticity0.4631110.024394-22.008746 H0: elast. = 1

\begin{tabular}{lllllllll}
\hline

Simple Linear Regression - Ungrouped Data \tabularnewline

Parameter & Value & S.E. & T-STAT & Notes \tabularnewline

Constant
165.550098 & & & \tabularnewline Beta1.8416830.09701018.984375 H0: beta = 0 \tabularnewline Elasticity0.4631110.024394-22.008746 H0: elast. = 1 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=49838&T=0

[TABLE]

[ROW][C]Simple Linear Regression - Ungrouped Data[/C][/ROW]

[ROW][C]Parameter[/C][C]Value[/C][C]S.E.[/C][C]T-STAT[/C][C]Notes[/C][/ROW]

[ROW][C]Constant[/C]
165.550098[/C][C][/C][C][/C][C][/C][/ROW] [ROW][C]Beta[/C]1.841683[/C]0.097010[/C]18.984375[/C] H0: beta = 0[/C][/ROW] [ROW][C]Elasticity[/C]0.463111[/C]0.024394[/C]-22.008746[/C] H0: elast. = 1[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=49838&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49838&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Simple Linear Regression - Ungrouped Data
ParameterValueS.E.T-STATNotes
Constant165.550098
Beta1.8416830.09701018.984375 H0: beta = 0
Elasticity0.4631110.024394-22.008746 H0: elast. = 1






Simple Linear Regression - Analysis of Variance
ANOVADFSum of SquaresMean Square
Regression1.000000432728.837589432728.837589
Residual358.000000429839.4221611200.668777
Total359.000000862568.2597502402.697102
F-TEST360.406505

\begin{tabular}{lllllllll}
\hline

Simple Linear Regression - Analysis of Variance \tabularnewline

ANOVA & DF & Sum of Squares & Mean Square \tabularnewline

Regression
1.000000432728.837589432728.837589 \tabularnewline Residual358.000000429839.4221611200.668777 \tabularnewline Total359.000000862568.2597502402.697102 \tabularnewline F-TEST360.406505 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=49838&T=1

[TABLE]

[ROW][C]Simple Linear Regression - Analysis of Variance[/C][/ROW]

[ROW][C]ANOVA[/C][C]DF[/C][C]Sum of Squares[/C][C]Mean Square[/C][/ROW]

[ROW][C]Regression[/C]
1.000000[/C]432728.837589[/C]432728.837589[/C][/ROW] [ROW][C]Residual[/C]358.000000[/C]429839.422161[/C]1200.668777[/C][/ROW] [ROW][C]Total[/C]359.000000[/C]862568.259750[/C]2402.697102[/C][/ROW] [ROW][C]F-TEST[/C]360.406505[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=49838&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49838&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Simple Linear Regression - Analysis of Variance
ANOVADFSum of SquaresMean Square
Regression1.000000432728.837589432728.837589
Residual358.000000429839.4221611200.668777
Total359.000000862568.2597502402.697102
F-TEST360.406505






Simple Linear Regression - Autocorrelation
StatisticValue
Durbin-Watson0.167253
Von Neumann Ratio0.167719
rho - Least Squares0.912188
rho - Maximum Likelihood0.919236
rho - Serial Correlation0.910897
rho - Goldberger0.915705

\begin{tabular}{lllllllll}
\hline

Simple Linear Regression - Autocorrelation \tabularnewline

Statistic & Value \tabularnewline

Durbin-Watson
0.167253 \tabularnewline Von Neumann Ratio0.167719 \tabularnewline rho - Least Squares0.912188 \tabularnewline rho - Maximum Likelihood0.919236 \tabularnewline rho - Serial Correlation0.910897 \tabularnewline rho - Goldberger0.915705 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=49838&T=2

[TABLE]

[ROW][C]Simple Linear Regression - Autocorrelation[/C][/ROW]

[ROW][C]Statistic[/C][C]Value[/C][/ROW]

[ROW][C]Durbin-Watson[/C]
0.167253[/C][/ROW] [ROW][C]Von Neumann Ratio[/C]0.167719[/C][/ROW] [ROW][C]rho - Least Squares[/C]0.912188[/C][/ROW] [ROW][C]rho - Maximum Likelihood[/C]0.919236[/C][/ROW] [ROW][C]rho - Serial Correlation[/C]0.910897[/C][/ROW] [ROW][C]rho - Goldberger[/C]0.915705[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=49838&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49838&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Simple Linear Regression - Autocorrelation
StatisticValue
Durbin-Watson0.167253
Von Neumann Ratio0.167719
rho - Least Squares0.912188
rho - Maximum Likelihood0.919236
rho - Serial Correlation0.910897
rho - Goldberger0.915705






Simple Linear Regression - Descriptive Statistics
StatisticValue
Mean X77.538167
Biased Variance X354.391669
Biased S.E. X18.825293
Mean Y308.350833
Biased Variance Y2396.022944
Biased S.E. Y48.949187
Mean F308.350833
Biased Variance F1202.024549
Biased S.E. F34.670226
Mean e0.000000
Biased Variance e1193.998395
Biased S.E. e1.826251

\begin{tabular}{lllllllll}
\hline

Simple Linear Regression - Descriptive Statistics \tabularnewline

Statistic & Value \tabularnewline

Mean X
77.538167 \tabularnewline Biased Variance X354.391669 \tabularnewline Biased S.E. X18.825293 \tabularnewline Mean Y308.350833 \tabularnewline Biased Variance Y2396.022944 \tabularnewline Biased S.E. Y48.949187 \tabularnewline Mean F308.350833 \tabularnewline Biased Variance F1202.024549 \tabularnewline Biased S.E. F34.670226 \tabularnewline Mean e0.000000 \tabularnewline Biased Variance e1193.998395 \tabularnewline Biased S.E. e1.826251 \tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=49838&T=3

[TABLE]

[ROW][C]Simple Linear Regression - Descriptive Statistics[/C][/ROW]

[ROW][C]Statistic[/C][C]Value[/C][/ROW]

[ROW][C]Mean X[/C]
77.538167[/C][/ROW] [ROW][C]Biased Variance X[/C]354.391669[/C][/ROW] [ROW][C]Biased S.E. X[/C]18.825293[/C][/ROW] [ROW][C]Mean Y[/C]308.350833[/C][/ROW] [ROW][C]Biased Variance Y[/C]2396.022944[/C][/ROW] [ROW][C]Biased S.E. Y[/C]48.949187[/C][/ROW] [ROW][C]Mean F[/C]308.350833[/C][/ROW] [ROW][C]Biased Variance F[/C]1202.024549[/C][/ROW] [ROW][C]Biased S.E. F[/C]34.670226[/C][/ROW] [ROW][C]Mean e[/C]0.000000[/C][/ROW] [ROW][C]Biased Variance e[/C]1193.998395[/C][/ROW] [ROW][C]Biased S.E. e[/C]1.826251[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=49838&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=49838&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Simple Linear Regression - Descriptive Statistics
StatisticValue
Mean X77.538167
Biased Variance X354.391669
Biased S.E. X18.825293
Mean Y308.350833
Biased Variance Y2396.022944
Biased S.E. Y48.949187
Mean F308.350833
Biased Variance F1202.024549
Biased S.E. F34.670226
Mean e0.000000
Biased Variance e1193.998395
Biased S.E. e1.826251


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):